SHW paper

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 06 Dec 2009 05:51:03 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/06/t12601040171hlkx0n1u35v86d.htm/, Retrieved Sun, 06 Dec 2009 13:53:49 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/06/t12601040171hlkx0n1u35v86d.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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8,3 0 8,8 8,9 7,5 0 8,3 8,8 7,2 0 7,5 8,3 7,4 0 7,2 7,5 8,8 0 7,4 7,2 9,3 0 8,8 7,4 9,3 0 9,3 8,8 8,7 0 9,3 9,3 8,2 0 8,7 9,3 8,3 0 8,2 8,7 8,5 0 8,3 8,2 8,6 0 8,5 8,3 8,5 0 8,6 8,5 8,2 0 8,5 8,6 8,1 0 8,2 8,5 7,9 0 8,1 8,2 8,6 0 7,9 8,1 8,7 0 8,6 7,9 8,7 0 8,7 8,6 8,5 0 8,7 8,7 8,4 0 8,5 8,7 8,5 0 8,4 8,5 8,7 0 8,5 8,4 8,7 0 8,7 8,5 8,6 0 8,7 8,7 8,5 0 8,6 8,7 8,3 0 8,5 8,6 8 0 8,3 8,5 8,2 0 8 8,3 8,1 0 8,2 8 8,1 0 8,1 8,2 8 0 8,1 8,1 7,9 0 8 8,1 7,9 0 7,9 8 8 0 7,9 7,9 8 0 8 7,9 7,9 0 8 8 8 0 7,9 8 7,7 0 8 7,9 7,2 0 7,7 8 7,5 0 7,2 7,7 7,3 0 7,5 7,2 7 0 7,3 7,5 7 0 7 7,3 7 0 7 7 7,2 0 7 7 7,3 1 7,2 7 7,1 1 7,3 7,2 6,8 1 7,1 7,3 6,4 1 6,8 7,1 6,1 1 6,4 6,8 6,5 1 6,1 6,4 7,7 1 6,5 6,1 7,9 1 7,7 6,5 7,5 1 7,9 7,7 6,9 1 7,5 7,9 6,6 1 6,9 7,5 6,9 1 6,6 6,9

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 2.75622369530088 -0.141185604893304X[t] + 1.39682018713845Y1[t] -0.719429746061353Y2[t] -0.0670407108398949M1[t] -0.080762823187288M2[t] -0.0522366748546463M3[t] -0.00507411743522141M4[t] + 0.701762994805734M5[t] -0.309620090779789M6[t] -0.0347808661624004M7[t] -0.059528429032278M8[t] + 0.0665520989852706M9[t] + 0.277841848919159M10[t] + 0.154825417140026M11[t] -0.00775463632460447t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 2.75622369530088 0.607804 4.5347 4.7e-05 2.4e-05 X -0.141185604893304 0.094346 -1.4965 0.142011 0.071005 Y1 1.39682018713845 0.109413 12.7665 0 0 Y2 -0.719429746061353 0.111227 -6.4681 0 0 M1 -0.0670407108398949 0.129837 -0.5163 0.608321 0.304161 M2 -0.080762823187288 0.133868 -0.6033 0.549553 0.274777 M3 -0.0522366748546463 0.1375 -0.3799 0.705931 0.352965 M4 -0.00507411743522141 0.13852 -0.0366 0.970953 0.485476 M5 0.701762994805734 0.13727 5.1123 7e-06 4e-06 M6 -0.309620090779789 0.144785 -2.1385 0.038338 0.019169 M7 -0.0347808661624004 0.128514 -0.2706 0.787995 0.393997 M8 -0.059528429032278 0.132029 -0.4509 0.654401 0.3272 M9 0.0665520989852706 0.136395 0.4879 0.628133 0.314067 M10 0.277841848919159 0.134369 2.0677 0.04486 0.02243 M11 0.154825417140026 0.135219 1.145 0.258694 0.129347 t -0.00775463632460447 0.002642 -2.9352 0.005386 0.002693 Multiple Linear Regression - Regression Statistics Multiple R 0.974890277812212 R-squared 0.950411053772772 Adjusted R-squared 0.932700715834476 F-TEST (value) 53.6641964192934 F-TEST (DF numerator) 15 F-TEST (DF denominator) 42 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.190545579175235 Sum Squared Residuals 1.52491994521548 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.3 8.57052125500866 -0.270521255008656 2 7.5 7.92257738737358 -0.422577387373576 3 7.2 7.18560762270153 0.0143923772984707 4 7.4 7.3815132845039 0.0184867154960978 5 8.8 8.57578872166635 0.224211278333653 6 9.3 9.36831331253777 -0.0683133125377741 7 9.3 9.32660634991389 -0.0266063499138856 8 8.7 8.93438927768873 -0.234389277688728 9 8.2 8.2146230570986 -0.0146230570986028 10 8.3 8.15140592477547 0.148594075224525 11 8.5 8.52003174841626 -0.0200317484162625 12 8.6 8.56487275777318 0.0351272422268162 13 8.5 8.48587348011026 0.0141265198897422 14 8.2 8.25277173811828 -0.0527717381182817 15 8.1 7.92644016859092 0.173559831409081 16 7.9 8.0419949947903 -0.141994994790301 17 8.6 8.5336564078851 0.0663435921149009 18 8.7 8.63617876618415 0.063821233815846 19 8.7 8.53934455094783 0.160655449052165 20 8.5 8.43489937714722 0.0651006228527828 21 8.4 8.27386123141247 0.126138768587527 22 8.5 8.48160027552018 0.0183997244798171 23 8.7 8.56245420073643 0.137545799263574 24 8.7 8.60729521009335 0.0927047899066517 25 8.6 8.38861391371658 0.211386086283422 26 8.5 8.22745514633074 0.272544853669264 27 8.3 8.18048761423107 0.119512385768936 28 8 8.01247447250433 -0.0124744725043315 29 8.2 8.43639684149142 -0.236396841491418 30 8.1 7.91245208082739 0.187547919172614 31 8.1 7.89596870119406 0.204031298805944 32 8 7.93540947660571 0.0645905233942918 33 7.9 7.9140533495848 -0.0140533495848079 34 7.9 8.04984941908638 -0.149849419086383 35 8 7.99102132558878 0.0089786744112186 36 8 7.968123290838 0.0318767091620054 37 7.9 7.82138496906736 0.0786150309326401 38 8 7.66022620168152 0.339773798318482 39 7.7 7.89262270700953 -0.192622707009535 40 7.2 7.44104159735669 -0.241041597356686 41 7.5 7.65754290352222 -0.15754290352222 42 7.3 7.4171661107843 -0.117166110784304 43 7 7.18905773783099 -0.189057737830992 44 7 6.88139543170725 0.118604568292753 45 7 7.2155502472186 -0.215550247218598 46 7.2 7.41908536082788 -0.219085360827881 47 7.3 7.42649272525853 -0.12649272525853 48 7.1 7.25970874129547 -0.159708741295472 49 6.8 6.83360638209715 -0.0336063820971483 50 6.4 6.53696952649589 -0.136969526495887 51 6.1 6.21484188746695 -0.114841887466954 52 6.5 6.12297565084478 0.37702434915522 53 7.7 7.59661512543492 0.103384874565084 54 7.9 7.96588972966638 -0.0658897296663827 55 7.5 7.64902266011323 -0.149022660113232 56 6.9 6.9139064368511 -0.0139064368510995 57 6.6 6.48191211468552 0.118087885314481 58 6.9 6.69805901979008 0.201940980209921 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.128552176858067 0.257104353716135 0.871447823141933 20 0.0677591735051601 0.135518347010320 0.93224082649484 21 0.0741543405728778 0.148308681145756 0.925845659427122 22 0.140114937601667 0.280229875203334 0.859885062398333 23 0.0830864282323503 0.166172856464701 0.91691357176765 24 0.0419937064239044 0.0839874128478089 0.958006293576096 25 0.0293622041009852 0.0587244082019705 0.970637795899015 26 0.0546873749382419 0.109374749876484 0.945312625061758 27 0.0446880471996913 0.0893760943993827 0.95531195280031 28 0.023294262550278 0.046588525100556 0.976705737449722 29 0.0994541164545314 0.198908232909063 0.900545883545468 30 0.0651694570028667 0.130338914005733 0.934830542997133 31 0.0863957666270655 0.172791533254131 0.913604233372935 32 0.073222526972664 0.146445053945328 0.926777473027336 33 0.092733058727208 0.185466117454416 0.907266941272792 34 0.108215040721592 0.216430081443184 0.891784959278408 35 0.0818890591873015 0.163778118374603 0.918110940812699 36 0.0665907197209642 0.133181439441928 0.933409280279036 37 0.0448371592432377 0.0896743184864753 0.955162840756762 38 0.366230909200154 0.732461818400307 0.633769090799846 39 0.85895499718349 0.28209000563302 0.14104500281651 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 1 0.0476190476190476 OK 10% type I error level 5 0.238095238095238 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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